Vehicle stability control with lateral dynamics feedback

ABSTRACT

A system and method for estimating vehicle side-slip velocity that includes measuring the lateral acceleration of the vehicle, measuring the yaw rate of the vehicle, measuring the longitudinal speed of the vehicle and measuring the steering angle of the vehicle. The measured longitudinal speed is corrected to provide a true longitudinal speed using a filter factor based on the vehicle-dependent parameters and a steering angle. A constant is defined based on the measured longitudinal speed and a function is defined based on the combination of the vehicle-dependent parameters and the lateral acceleration. Side-slip acceleration is calculated using the measured lateral acceleration, the true longitudinal speed, the yaw rate, the constant and the function.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to a system for estimating vehicleside-slip and, more particularly, to a system for estimating vehicleside-slip that uses vehicle lateral acceleration and vehicle-dependentparameters.

2. Discussion of the Related Art

Various vehicle stability control systems are known in the art thatimprove driver convenience, safety and comfort. These stability controlsystems typically employ differential braking and/or active front andrear wheel steering to provide the stability control. The stabilitycontrol systems generally operate within a linear vehicle operatingregion, where vehicle states define the behavior of the vehicle. Thevehicle states are generally determined from measured parameters, suchas vehicle yaw rate, vehicle longitudinal velocity and vehicle lateralvelocity.

Vehicle side-slip velocity is one of the key states for determiningvehicle dynamics, kinematics and control for these types of stabilitycontrol systems. Vehicle side-slip velocity is defined as the lateralspeed at the vehicle's center of gravity in a direction perpendicular tothe vehicle longitudinal velocity. The vehicle side-slip velocitycombined with the vehicle longitudinal velocity defines a vehicle vectorvelocity in the vehicle traveling direction. However, the measurement ofvehicle side-slip angle, which requires a measurement of vehicleside-slip velocity, requires special sensors that are very expensive.Therefore, vehicle stability control systems typically estimate vehicleside-slip velocity. Particularly, vehicle control systems calculate thevehicle side-slip velocity to determine an error so that the vehicle canbe controlled to reduce the side-slip error to zero. However, vehicleside-slip velocity is difficult to accurately calculate because it istypically very small within the linear operating region of the vehicle.

One known method for estimating vehicle side-slip velocity that useslimited-bandwidth integration is disclosed in U.S. Pat. No. 6,819,998,titled Method and Apparatus for Vehicle Stability Enhancement System,issued Nov. 16, 2004 to Lin et al., assigned to the Assignee of thisinvention and herein incorporated by reference. As a result, reasonablyaccurate side-slip estimations can be provided without expensiveside-slip velocity sensors. However, improvements can be made forestimating vehicle side-slip velocity.

SUMMARY OF THE INVENTION

In accordance with the teachings of the present invention, a system andmethod for estimating vehicle side-slip velocity using vehicle lateralacceleration and vehicle-dependent parameters is disclosed. The methodincludes measuring the lateral acceleration of the vehicle, measuringthe yaw rate of the vehicle, measuring the longitudinal speed of thevehicle and measuring the steering angle of the vehicle. The measuredlongitudinal speed of the vehicle is corrected to provide a truelongitudinal speed using a filter factor based on the vehicle-dependentparameters and the steering angle. A constant is defined based on themeasured longitudinal speed of the vehicle and a function is definedbased on a combination of the vehicle-dependent parameters and thelateral acceleration of the vehicle. Side-slip acceleration iscalculated using the measured lateral acceleration, the truelongitudinal speed, the yaw rate, the constant and the function.

Additional features of the present invention will become apparent fromthe following description and appended claims, taken in conjunction withthe accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plan view of a vehicle including a rear-wheel steeringcontrol system and a vehicle stability enhancement system;

FIG. 2 is a block diagram of the vehicle stability enhancement systemshown in FIG. 1 including a side-slip velocity estimation processor,according to an embodiment of the present invention;

FIG. 3 is a block diagram of the side-slip velocity estimation processorshown in FIG. 2;

FIG. 4 is a block diagram of a sub-system for generating a filteringfactor for determining the vehicle side-slip velocity estimation; and

FIG. 5 is a block diagram of a sub-system for determining a truelongitudinal speed value for determining the vehicle side-slip velocityestimation of the invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The following discussion of the embodiments of the invention directed toa system and method for estimating vehicle side-slip velocity is merelyexemplary in nature, and is in no way intended to limit the invention orits applications or uses.

FIG. 1 is a plan view of a vehicle 10 including front wheels 12 and 14and rear wheels 16 and 18. The vehicle 10 includes vehicle stabilitycontrol provided by a vehicle stability enhancement system (VSES) 22 anda rear-wheel steering control system 24. The vehicle 10 includes sensorsfor measuring various vehicle states, including a hand-wheel anglesensor 28 for measuring the angle of a vehicle hand-wheel 30 to providea signal indicative of the steering angle for steering the front wheels12 and 14. Further, the vehicle 10 includes a speed sensor 34 forproviding a signal indicative of the vehicle longitudinal speed, a yawrate sensor 36 for providing a signal indicative of the yaw rate of thevehicle 10 and a lateral acceleration sensor 38 for providing a signalindicative of the lateral acceleration of the vehicle 10. The VSES 22receives the hand-wheel angle signal, the longitudinal speed signal, thevehicle yaw rate signal and the vehicle lateral acceleration signal, anduses a stability control algorithm based on the measured signals andother vehicle parameters to provide differential braking to the wheels12-18, and thus, stability control for the vehicle 10. Many suitablecontrol algorithms are known in the art that provide stability controlto reduce vehicle roll, side-slip, etc.

The rear-wheel steering control system 24 receives the hand-wheel anglesignal and the longitudinal speed signal to provide a rear-wheel commandsignal to a rear-wheel steering actuator 42 to steer the rear wheels 16and 18. Many suitable control algorithms are known in the art, bothopen-loop and closed-loop including feedback, to provide rear-wheelsteering assist.

As mentioned above, vehicle side-slip velocity is one of the vehicleparameters used in most, if not all, vehicle stability systems. As willbe discussed in detail below, the present invention proposes a newtechnique for calculating an estimation of the vehicle side-slipvelocity using a filtering factor based on vehicle-dependent parametersand lateral acceleration.

FIG. 2 is a block diagram of the VSES 22. The VSES 22 includes a commandinterpreter 52 that receives the hand-wheel angle signal from thehand-wheel angle sensor 28 on line 54 and the longitudinal speed signalfrom the vehicle speed sensor 34 on line 56. The command interpreter 52provides a desired yaw-rate command signal and a desired side-slipvelocity command signal based on the hand-wheel angle signal and thelongitudinal speed signal. Various algorithms are known in the art forproviding the yaw-rate command signal and the desired side-slip velocitycommand signal in a command interpreter of this type. U.S. Pat. No.6,122,584, titled Brake System Control, issued Sep. 19, 2000 to Lin etal., discloses a command interpreter that calculates a desired side-slipvelocity that can be used for determining the desired side-slip velocitycommand signal.

The VSES 22 also includes a yaw-rate feedback control processor 58 thatreceives the yaw rate signal from the yaw-rate sensor 36 on line 60 andthe yaw-rate command signal from the command interpreter 52. Theyaw-rate feedback control processor 58 uses any suitable algorithm, manyof which are known in the art, to provide a yaw-rate control componentsignal to minimize the difference between the measured vehicle yaw rateand the desired vehicle yaw rate.

The VSES 22 also includes a side-slip velocity estimation processor 62that receives the yaw-rate signal on line 60, the longitudinal speedsignal on line 56 and the lateral acceleration signal from the lateralacceleration sensor 38 on line 64. The side-slip estimation processor 62generates an estimated side-slip of the vehicle 10 in a new and novelmanner based on an algorithm of the invention as will be discussed indetail below.

The VSES 22 also includes a side-slip velocity control processor 68 thatreceives the side-slip velocity command signal from the commandinterpreter 52 and the estimated side-slip velocity signal from theside-slip velocity estimation processor 62. The side-slip velocitycontrol processor 68 generates a side-slip velocity control componentsignal to minimize the difference between the desired side-slip velocityof the vehicle and the estimated side-slip velocity of the vehicle.

The yaw-rate control component signal from the yaw-rate feedback controlprocessor 58 and the side-slip velocity control component signal fromthe side-slip velocity control processor 68 are added by an adder 70that generates the actuator control command that provides differentialbraking for the wheels 12-18 so that the measured yaw-rate signal istracking the yaw-rate command signal and the estimated side-slipvelocity signal is tracking the side-slip velocity command signal.

The '998 patent referenced above discloses a VSES that would employ acommand interpreter, a yaw-rate feedback control processor, a side-slipvelocity estimation processor and a side-slip velocity controlprocessor. The present invention is an improvement over the VSESdisclosed by the '998 patent because it calculates the side-slipvelocity estimation signal differently in the side-slip velocityestimation processor 62.

A more detailed block diagram of the side-slip velocity estimationprocessor 62 is shown in FIG. 3. An estimation of side-slip accelerationprocessor 80 receives the yaw-rate signal on line 82, the lateralacceleration signal on line 84 and the longitudinal speed signal on line86. The estimation of side-slip acceleration processor 80 calculates anestimated side-slip acceleration signal {dot over (V)}_(y) _(—)_(estimated), as will be discussed below.

The processor 80 determines an error signal E_(Vy) as the differencebetween the desired side-slip velocity signal V_(y) _(—) _(desired) fromthe command interpreter 52 and a feedback side-slip velocity signalV_(y) _(—) _(feedback) by the equation:E_(Vy=)V_(y) _(—) _(desired−)V_(y) _(—) _(feedback)  (1)

To determine the feedback side-slip velocity signal V_(y) _(—)_(feedback), the '998 patent proposes a method of limited-bandwidthintegration of the measured side-slip acceleration {dot over (V)}_(y)_(—) _(measured) to compensate for the negative effects of sensor biasand noise. The true side-slip acceleration {dot over (V)}_(y), withsensor bias B, can be represented as:{dot over (V)}_(y)=A_(y) _(—) _(measured) −r _(—) _(measured)V_(x) _(—)_(measured)+B={dot over (V)}_(y) _(—) _(measured)+B  (2)Where A_(y) _(—) _(measured) is the lateral acceleration signal from thelateral acceleration sensor 38, r _(—) _(measured) is the yaw-ratesignal from the yaw-rate sensor 36, V_(x) _(—) _(measured) is thelongitudinal speed signal from the vehicle speed sensor 34 and {dot over(V)}_(y) _(—) _(measured) is the measured side-slip acceleration of thevehicle 10.

Equation (2) can be converted to equation (3) as:{dot over (V)}_(y) _(—) _(measured)=A_(y) _(—) _(measured) −r _(—)_(measured)V_(x) _(—) _(measured)  (3)

Equation (3) is valid when the vehicle is under limited roll andside-slip motion. When the intensity of either motion is increasing, themeasured side-slip acceleration will exhibit an increasing error fromthe “true” vehicle side-slip acceleration. As a result, the estimatedside-slip velocity based on integration of the estimated side-slipacceleration signal may also show an increase in error. Because the rollangle is not readily available from sensor measurements, the lateralacceleration information is used instead of the roll angle to accountfor the roll motion effect, according to the invention. To compensatefor the roll motion effect, the present invention proposes to modifyequation (3) as:{dot over (V)}_(y) _(—) _(estimated)={dot over (V)}_(y) _(—) _(measured)−kƒ(A_(y) _(—) _(measured))  (4)Where k is a constant and ƒ is a non-linear function of the measuredlateral acceleration signal A_(y) _(—) _(measured).

Both the constant k and the function ƒ are vehicle dependent and can bederived experimentally. For a typical SUV, the speed-dependent values inTable I below can be used for the constant k.

TABLE I Speed (kph) 0 40 80 100 140 K 1.2 1.2 1.1 1.0 0.9

The function ƒ is defined as having the following relationship to themeasured lateral acceleration signal A_(y) _(—) _(measured) as:

$\begin{matrix}{f = \frac{{b_{1}A_{y\_ measured}} - b_{2}}{s^{2} + {a_{1}s} + a_{2}}} & (5)\end{matrix}$Where b₁, b₂, a₁, a₂ are vehicle-dependent parameters that can also bederived experimentally and s is the Laplace operator.

For a typical SUV, the values in Table II for b₁, b₂, a₁, a₂ can be useddepending on the measured lateral acceleration signal A_(y) _(—)_(measured).

TABLE II A_(y) _(—) measured (g) <0.9 >=0.9 b₁ 0.82 0.55 b₂ 0 5.91 a₁3.16 0 a₂ 73.57 0

FIG. 4 is a block diagram of a sub-system 90 in the estimation ofside-slip acceleration processor 80 for determining the product of theconstant k and the function ƒ to determine the estimated side-slipacceleration signal {dot over (V)}_(y) _(—) _(estimated) in equation(4). The measured lateral acceleration signal A_(y) _(—) _(measured)from the lateral acceleration sensor 38 on line 92 is provided to afunction processor 94, a function processor 96 and a switch 98. If themeasured lateral acceleration signal A_(y) _(—) _(measured) is below 0.9g, then the switch 98 switches to the output of the function processor94 that generates the function ƒ using the values b₁, b₂, a₁ and a₂ inthe first column of Table II. Likewise, if the measured lateralacceleration signal A_(y) _(—) _(measured) is greater than or equal to0.9 g, then the switch 98 switches to the output of the functionprocessor 96 that generates the function ƒ using the values for b₁, b₂,a₁ and a₂ in the second column of Table II. The longitudinal speedsignal V_(y) _(—) _(measured) from the vehicle speed sensor 34 isprovided to a look-up table 100 on line 102. The look-up table 100provides the constant k from Table I based on the vehicle speed. Thefunction ƒ from the switch 98 and the constant k from the look-up table100 are applied to a multiplier 104 that multiplies the signals toprovide a side-slip correction term for equation (4).

According to the invention, the longitudinal speed signal V_(x) _(—)_(measured) can be processed to consider the effect of large steeringangles to provide a true longitudinal speed signal V_(x) _(—) _(true).FIG. 5 is a block diagram of a sub-system 110 in the estimation ofside-slip acceleration processor 80 for calculating the finallongitudinal velocity that takes into account the steering angle. Thelongitudinal speed signal V_(x) _(—) _(measured) is applied to a filterprocessor 112 on line 114. The filter processor 112 uses the followingequation (6) to generate a filtered longitudinal speed signal V_(x) _(—)_(measured) _(—) _(filter).

$\begin{matrix}{V_{{x\_ measured}{\_ filter}} = {\frac{d}{s^{2} + {c_{1}s} + c_{2}}V_{x\_ measured}}} & (6)\end{matrix}$Where d, c₁ and c₂ are vehicle-dependent parameters. For a typical SUV,d=39.5, c₁=8.9 and c₂=39.5.

The filtered speed signal V_(x) _(—) _(measured) _(—) _(filter) is thencorrected using the steering angle to provide the actual vehiclelongitudinal direction. Particularly, the hand-wheel angle signal fromthe hand-wheel angle sensor 28 is provided to a gear ratio gainprocessor 116 on line 118. The gain processor 116 adds a gear ratio gainto the hand-wheel angle signal for the front wheels 12 and 14. Thesteering angle signal from the gain processor 116 is then applied to acosine processor 120 that provides the steering angle correction signal.The steering angle correction signal from the cosine processor 120 andthe longitudinal filtered signal V_(x) _(—) _(measured) _(—) _(filter)from the processor 112 are multiplied by a multiplier 122 to provide thetrue longitudinal speed signal V_(x) _(—) _(true).

The estimation of side-slip acceleration processor 80 then combinesequations (4) and (5) with the true longitudinal speed signal V_(x) _(—)_(true) to provide an accurate estimation of the side-slip acceleration{dot over (V)}_(y) _(—) _(estimated) as:{dot over (V)}_(y) _(—) _(estimated)=A_(y) _(—) _(measured) −r _(—)_(measured)V_(x) _(—) _(true) −kƒ(A_(y) _(—) _(measured))  (7)

The output of the estimation of side-slip acceleration processor 80 isthe estimated side-slip acceleration signal {dot over (V)}_(y) _(—)_(estimated). The estimated side-slip acceleration signal {dot over(V)}_(y) _(—) _(estimated) is then integrated by a frequency integrator132 to give the estimated side-slip velocity. During those times thatthe vehicle 10 is not exhibiting side-slip, and the signal {dot over(V)}_(y) _(—) _(estimated) is near zero, the integration of theestimated side-slip acceleration signal in the frequency integrator 132is reset to zero by a reset logic processor 130, as is well understoodin the art. The reset logic processor 130 receives the hand-wheel anglesignal on line 134.

The foregoing discussion discloses and describes merely exemplaryembodiments of the present invention. One skilled in the art willreadily recognize from such discussion and from the accompanyingdrawings and claims that various changes, modifications and variationscan be made therein without departing from the spirit and scope of theinvention as defined in the following claims.

1. A method for estimating side-slip of a vehicle, said methodcomprising: measuring the lateral acceleration of the vehicle andproviding a measured lateral acceleration signal; measuring the yaw rateof the vehicle and providing a measured yaw rate signal; measuring thelongitudinal speed of the vehicle and providing a measured longitudinalspeed signal; correcting the measured longitudinal speed signal toprovide a true longitudinal speed signal; defining a constant based onthe measured longitudinal speed signal; defining a function based onpredetermined vehicle-dependent parameters and the measured lateralacceleration signal; and estimating the side-slip by combining themeasured lateral acceleration signal, the measured yaw rate signal, thetrue longitudinal speed signal, the constant and the function.
 2. Themethod according to claim 1 wherein estimating the side-slip includesusing the equation:{dot over (V)}_(y) _(—) _(estimated)=A_(y) _(—) _(measured) −r _(—)_(measured) V_(x) _(—) _(true) −kƒ(A_(y) _(—) _(measured)) where {dotover (V)}_(y) _(—) _(estimated) is estimated side-slip acceleration,A_(y) _(—) _(measured) is the measured lateral acceleration signal,r_(—) _(measured) is the measured yaw rate signal, V_(x) _(—) _(true) isthe true longitudinal speed signal, k is the constant and ƒ is thefunction.
 3. The method according to claim 1 wherein correcting themeasured longitudinal speed signal includes filtering the measuredlongitudinal speed signal using vehicle-dependent parameters to providea filtered longitudinal speed signal.
 4. The method according to claim 3wherein filtering the measured longitudinal speed signal includes usingthe equation:$V_{{x\_ measured}{\_ filter}} = {\frac{d}{s^{2} + {c_{1}s} + c_{2}}V_{x\_ measured}}$where V_(x) _(—) _(measured) _(—) _(filter) is the filtered longitudinalspeed signal, V_(x) _(—) _(measured) is the measured longitudinal speedsignal, s is the Laplace operator and d, c₁ and c₂ are thevehicle-dependent parameters.
 5. The method according to claim 3 whereincorrecting the measured longitudinal speed signal further includesproviding a steering angle correction to the filtered longitudinal speedsignal.
 6. The method according to claim 5 wherein correcting thelongitudinal speed signal includes providing a hand-wheel signalindicative of the position of a vehicle hand-wheel, ratioing thehand-wheel signal to provide a ratio signal and multiplying the ratiosignal by the filtered longitudinal speed signal.
 7. The methodaccording to claim 1 wherein defining the function includes using afirst set of vehicle-dependent parameters if the measured longitudinalspeed signal is below a predetermined value and using a second set ofvehicle-dependent parameters if the measured longitudinal speed signalis greater than or equal to the predetermined value.
 8. The methodaccording to claim 1 wherein defining the function include using theequation:$f = \frac{{b_{1}A_{y\_ measured}} - b_{2}}{s^{2} + {a_{1}s} + a_{2}}$where ƒ is the function, A_(y) _(—) _(measured) is the measured lateralacceleration signal, s is the Laplace operator, and a₁, a₂, b₁ and b₂are the vehicle-dependent parameters.
 9. The method according to claim 1wherein estimating the side-slip includes multiplying the constant andthe function.
 10. The method according to claim 1 wherein the method isused in a stability control system for the vehicle.
 11. A system forestimating side-slip of a vehicle, said system comprising: a lateralacceleration sensor for measuring the lateral acceleration of thevehicle and providing a measured lateral acceleration signal; a yaw ratesensor for measuring the yaw rate of the vehicle and providing ameasured yaw rate signal; a longitudinal speed sensor for measuring thelongitudinal speed of the vehicle and providing a measured longitudinalspeed signal; and a side-slip estimation processor for estimating theside-slip of the vehicle, said processor correcting the measuredlongitudinal speed signal to provide a true longitudinal speed signal,defining a constant based on the measured longitudinal speed signal, anddefining a function based on predetermined vehicle-dependent parametersand the measured lateral acceleration signal, said processor estimatingthe side-slip by combining the measured lateral acceleration signal, themeasured yaw rate signal, the true longitudinal speed signal, theconstant and the function.
 12. The system according to claim 11 whereinthe side-slip estimation processor estimates the side-slip using theequation:{dot over (V)}_(y) _(—) _(estimated)=A_(y) _(—) _(measured) −r _(—)_(measured) V_(x) _(—) _(true) −kƒ(A_(y) _(—) _(measured)) where {dotover (V)}_(y) _(—) _(estimated) is estimated side-slip acceleration,A_(y) _(—) _(measured) is the measured lateral acceleration signal,r_(—) _(measured) is the measured yaw rate signal, V_(x) _(—) _(true) isthe true longitudinal speed signal, k is the constant and ƒ is thefunction.
 13. The system according to claim 11 wherein the side-slipestimation processor corrects the measured longitudinal speed signal byfiltering the measured longitudinal speed signal using vehicle-dependentparameters to provide a filtered longitudinal speed signal.
 14. Thesystem according to claim 13 wherein the side-slip estimation processorfilters the measured longitudinal speed signal using the equation:$V_{{x\_ measured}{\_ filter}} = {\frac{d}{s^{2} + {c_{1}s} + c_{2}}V_{x\_ measured}}$where V_(x) _(—) _(measured) _(—) _(filter) is the filtered longitudinalspeed signal, V_(x) _(—) _(measured) is the measured longitudinal speedsignal, s is the Laplace operator and d, c₁ and c₂ are thevehicle-dependent parameters.
 15. The system according to claim 13wherein the side-slip estimation processor corrects the measuredlongitudinal speed signal by providing a steering angle correction tothe filtered longitudinal speed signal.
 16. The system according toclaim 15 wherein the side-slip estimation processor corrects thelongitudinal speed signal by providing a hand-wheel signal indicative ofthe position of a vehicle hand-wheel, ratioing the hand-wheel signal toprovide a ratio signal and multiplying the ratio signal by the filteredlongitudinal speed signal.
 17. The system according to claim 11 whereinthe side-slip estimation processor defines the function by using a firstset of vehicle-dependent parameters if the measured longitudinal speedsignal is below a predetermined value and using a second set ofvehicle-dependent parameters if the measured longitudinal speed signalis greater than or equal to the predetermined value.
 18. The systemaccording to claim 11 wherein the side-slip estimation processor definesthe function by using the equation:$f = \frac{{b_{1}A_{y\_ measured}} - b_{2}}{s^{2} + {a_{1}s} + a_{2}}$where ƒ is the function, A_(y) _(—) _(measured) is the measured lateralacceleration signal, s is the Laplace operator, and a₁, a₂, b₁ and b₂are the vehicle-dependent parameters.
 19. The system according to claim11 wherein the side-slip estimation processor estimates the side-slip bymultiplying the constant and the function.
 20. A system for estimatingside-slip of a vehicle, said system comprising: a lateral accelerationsensor for measuring the lateral acceleration of the vehicle andproviding a measured lateral acceleration signal; a yaw rate sensor formeasuring the yaw rate of the vehicle and providing a measured yaw ratesignal; a longitudinal speed sensor for measuring the longitudinal speedof the vehicle and providing a measured longitudinal speed signal; ahand-wheel angle sensor for measuring the position of a vehiclehand-wheel and providing a hand-wheel signal; and a side-slip estimationprocessor for estimating the side-slip of the vehicle, said side-slipestimation processor correcting the measured longitudinal speed signalto provide a true longitudinal speed signal by filtering the measuredlongitudinal speed signal using vehicle-dependent parameters to providea filtered longitudinal speed signal and correcting the filteredlongitudinal speed signal to provide a steering angle correction usingthe hand-wheel signal, said side-slip estimation processor defining aconstant based on the measured longitudinal speed signal and defining afunction based on the predetermined vehicle-dependent parameters and themeasured lateral acceleration signal, said side-slip estimationprocessor estimating side-slip acceleration of the vehicle using anequation that combines the measured lateral acceleration signal, themeasured yaw rate signal, the true longitudinal speed signal, theconstant and the function, wherein the equation multiplies the constantand the function.
 21. The system according to claim 11 wherein theside-slip estimation processor estimates the side-slip using theequation:{dot over (V)}_(y) _(—) _(estimated)=A_(y) _(—) _(measured) −r _(—)_(measured) V_(x) _(—) _(true) −kƒ(A_(y) _(—) _(measured)) where {dotover (V)}_(y) _(—) _(estimated) is estimated side-slip acceleration,A_(y) _(—) _(measured) is the measured lateral acceleration signal,r_(—) _(measured) is the measured yaw rate signal, V_(x) _(—) _(true) isthe true longitudinal speed signal, k is the constant and ƒ is thefunction.
 22. The system according to claim 13 wherein the side-slipestimation processor filters the measured longitudinal speed signalusing the equation:$V_{{x\_ measured}{\_ filter}} = {\frac{d}{s^{2} + {c_{1}s} + c_{2}}V_{x\_ measured}}$where V_(x) _(—) _(measured) _(—) _(filter) is the filtered longitudinalspeed signal, V_(x) _(—) _(measured) is the measured longitudinal speedsignal, s is the Laplace operator and d, c₁ and c₂ are thevehicle-dependent parameters.
 23. The system according to claim 11wherein the side-slip estimation processor defines the function by usingthe equation:$f = \frac{{b_{1}A_{y\_ measured}} - b_{2}}{s^{2} + {a_{1}s} + a_{2}}$where ƒ is the function, A_(y) _(—) _(measured) is the measured lateralacceleration signal, s is the Laplace operator, and a₁, a₂, b₁ and b₂are the vehicle-dependent parameters.
 24. The system according to claim11 wherein the side-slip estimation processor defines the function byusing a first set of vehicle-dependent parameters if the measuredlongitudinal speed signal is below a predetermined value and using asecond set of vehicle-dependent parameters if the measured longitudinalspeed signal is greater than or equal to the predetermined value.